Abstract

Starting from the standard three-wave SBS coupled equations, we derive a novel expression describing Brillouin interaction between a pulsed pump wave with a finite cw component, and a Stokes continuous wave counter-propagating along a single-mode optical fiber. The derived integral equation relates the time-domain Stokes beam amplification to the Brillouin frequency distribution. The proposed model permits an accurate description of the Brillouin interaction even for arbitrarily-shaped pump pulses, and can be efficiently employed for improving the accuracy and the resolution of SBS-based distributed sensors. The validity and the limits of the proposed model are numerically analyzed and discussed.

Stokes amplification time-domain waveforms, as calculated by solving the full model of Eq.s (1) (dashed blue lines) and the model of Eq. (7) (solid red lines). The inset shows a zoom-in view of the perturbed region, at Δ=30 MHz. Solutions are calculated for L=50 m, τP=10 ns, and ER=20 dB.

Stokes amplification time-domain waveforms, as calculated by solving the full model of Eq.s (1) (dashed blue lines) and the model of Eq. (6), in which pump depletion is taken into account (solid red lines). Solutions are calculated for L=50 m, τP=10 ns, and ER=20 dB.